312 NEW SERIES for the 
Inftead of S, we now fabftitute i in this expreffion s, - 5; salt ae 
4 
&c. fucceflively, and multiply the refults by the terms of the 
feries 1, ia > ? &c. fo as to form the following feries of 
equations, the number of which is 2. 
I I I I 
z ee se 
tans 2 Can Sst A 2 2 
I I I I 
———S a es St ole =(s = 
2 tan’ +s 4 tan’zs5 3 4° x 2.4 
I I 2 
———— Si et 4 tan*= 5 
\ 4 tants S*tan’zs 48 8 hog ap 2.4° 
I I Pn I 
ae ee tans pleat 
8* tan’ > s 16*tan’ sy 5 oe 4* 16 2.4” 
&e. 
From thefe, by: proceeding in all refpects as in the atticle 
above quoted, that is, by adding, and rejecting what is common 
to each fide of the fum, we get 
(ees 
an tan? 
2 git 
I = I 21 I I I 
= ~ tan — 5 -+—tan? ne = tan’ Eas, a ae 
I I I I 
Bice Tt og ie Roaagl yc 
Now, 
